18 citations · 86 across the 27 of their papers we have counts for
11 papers · 1 filter
Closing the gap around the essential minimum of height functions with linear programming
José Burgos Gil, Ricardo Menares, Binggang Qu +1
For many common height functions, it is notoriously hard to compute the essential minimum. Nevertheless there are two classical methods, one giving lower bounds and the other givin…
On the height of the universal abelian variety
José Ignacio Burgos Gil, Jürg Kramer
In this paper we extend the arithmetic intersection theory of adelic divisors on quasiprojective varieties developed by X. Yuan and S. W. Zhang to cover certain adelic arithmetic d…
Tempered currents and Deligne cohomology of Shimura varieties, with an application to
José Ignacio Burgos Gil, Antonio Cauchi, Francesco Lemma +1
We provide a new description of Deligne-Beilinson cohomology for any Shimura variety in terms of tempered currents. This is particularly useful for computations of regulators of mo…
On the essential minimum of Faltings' height
José Burgos Gil, Ricardo Menares, Juan Rivera-Letelier
We study the essential minimum of the (stable) Faltings height on the moduli space of elliptic curves. We prove that, in contrast to the Weil height on a projective space and the N…
The distribution of Galois orbits of points of small height in toric varieties
José Ignacio Burgos Gil, Patrice Philippon, Juan Rivera-Letelier +1
We address the distribution properties of points of small height on proper toric varieties and applications to the related Bogomolov property. We introduce the notion of monocritic…
Height of varieties over finitely generated fields
Jose Ignacio Burgos Gil, Patrice Philippon, Martin Sombra
We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This…